Emily is 20 years older than Luis. Eighteen years ago, Emily was 5 times as old as Luis. How old is Luis now?
Answer: We can use the given information to write down two equations that describe the ages of Emily and Luis. Let Emily's current age be $e$ and Luis's current age be $l$ The information in the first sentence can be expressed in the following equation: $e = l + 20$ Eighteen years ago, Emily was $e - 18$ years old, and Luis was $l - 18$ years old. The information in the second sentence can be expressed in the following equation: $e - 18 = 5(l - 18)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $l$ , it might be easiest to use our first equation for $e$ and substitute it into our second equation. Our first equation is: $e = l + 20$ . Substituting this into our second equation, we get the equation: $(l + 20)$ $-$ $18 = 5(l - 18)$ which combines the information about $l$ from both of our original equations. Simplifying both sides of this equation, we get: $l + 2 = 5 l - 90$ Solving for $l$ , we get: $4 l = 92$ $l = 23$.